Approximate third-order function generator, temperature compensation quartz oscillation circuit made by using the same, and temperature compensation method

ABSTRACT

An approximate third-order function generator includes first, second, and third amplifiers, each receiving a common input signal and different fixed level signals. The three fixed level signals received respectively by the amplifiers sequentially increase in level. Each amplifier has an input-output characteristic whereby a non-inverted or inverted output signal is provided based on the common input signal and the fixed level signal. The fourth amplifier receives the same fixed level signal as the second amplifier and has an input-output characteristic in which a non-inverted or inverted output signal is provided based on the common input signal and the fixed level signal. The outputs of the first, third and fourth amplifiers have the same polarity, while that of the second amplifier is inverted. The output signals from the first, second, third and fourth amplifiers are added to generate a third-order function component free from the first-order component.

TECHNICAL FIELD

The present invention relates to an approximate third-order function generator, for example, for use with a temperature compensated crystal oscillator, a temperature compensated crystal oscillation circuit made by using the function generator, and a temperature compensation method.

BACKGROUND ART

An example of an approximate third-order function generator of this type is the invention described, for example, on Japanese Patent Laid-Open No. 9-55624 which the present applicant proposed before.

This prior art discloses an approximate third-order curve generation circuit which comprises three differential amplifiers, each comprising a pair of MOS field effect transistors receiving a common first-order input signal and a fixed level signal, the respective fixed level signals to the three differential amplifiers being different in level, and providing a non-inverted output and an inverted output, and the non-inverted outputs and the inverted outputs from the three differential amplifiers being added respectively in group.

However, although the above prior art generator can generate an approximate third-order function, it cannot arbitrarily control its variable independently, which is a unsolved problem.

A general form of the third-order function is represented by:

f(x)=a ₃ x ³ +a ₂ x ² +a ₁ x+a ₀  (1)

By transforming the variable in the expression (1), the expression (1) is rewritten as follows:

f(x)=a ₃′(x−x ₀)³ +a ₁′(x−x ₀)+a ₀′

a ₃ =a ₃′

a ₂3′x ₀

a ₁=3a ₃ ′x ₀ ² +a ₁′

a ₀ =a ₀ ′−a ₃ x ₀ ³ −a ₁ ′x ₀  (2)

Since in the prior art the three differential amplifiers are used to generate an approximate third-order function, the output approximate third-order function is shown in FIG. 15, which is represented by the following expression (3).

This expression (3) contains a second term component of the expression (2) thereby and variables a₃′ and a₁′ in the expression (2) cannot be controlled independently, which is an unsolved problem.

f(x)=α{a ₃″(x−x ₀)³ +a ₁″(x−x ₀)}+a″  (3)

Especially, when the approximate third-order function generator is used for temperature compensation of an voltage-controlled crystal oscillation circuit, an approximate third-order function which compensates a temperature characteristics of the crystal oscillator is required to be generated, but an accurate temperature compensated crystal oscillation circuit cannot be constituted, which is an unsolved problem.

DISCLOSURE OF THE INVENTION

The present invention is made in view of those unsolved problems with the prior art. It is a first object of the present invention to provide an approximate third-order function generator capable of accurately outputting only a first term component of the expression (2) and controlling the respective variables independently.

A second object of the present invention is to provide a temperature compensated crystal oscillation circuit which uses an approximate third-order function generator to perform accurate temperature compensation.

A third object of the present invention. is to provide a method of performing temperature compensation for a temperature compensated crystal oscillation circuit.

In order to achieve the first object, an approximate third-order function generator of claim 1 comprises a first amplifier, a second amplifier and a third amplifier each receiving a common input signal and a different fixed level signal, the three different fixed level signals received respectively by the first, second and third amplifiers sequentially increasing in level in this order, each amplifier having an input-output characteristics in which a non-inverted or inverted output signal is provided based on the common input signal and the fixed level signal concerned, that amplifier also having a function to limit the output signal to within a range defined by a maximum predetermined value and a minimum predetermined value; a fourth amplifier receiving the common input signal and the same fixed level signal as the second amplifier receives, the fourth amplifier having an input-output characteristics in which a non-inverted or inverted output signal is provided based on the common input signal and the fixed level signal concerned, and having a function to limit the output signal to within a range defined by a maximum predetermined value and a minimum predetermined value; and a fixed level signal generation circuit for supplying the fixed level signals having the different fixed levels to the first, second, third, and fourth amplifiers, respectively, the output characteristics of the first, third and fourth amplifiers being set so as to have the same polarity, the output characteristics of the second amplifier being set so as to be reverse to those of the first, third and fourth amplifiers, wherein the output signals from the first, second, third and fourth amplifiers being added to generate a third-order function component free from a first-order component.

In the invention of claim 1, the second amplifier which has a characteristics reverse to those of the first, third and fourth amplifiers is provided, so that only a third-order component free from the first-order component as the first term of the expression (2) produced by the first, second and third amplifiers can be generated. Thus, the variables of the first and second terms of the expression (2) can be controlled independently.

An approximate third-order function generator of claim 2 comprises a third-order component generation unit which includes a third-order component generation circuit having the composition of claim 1 supplied with an input added voltage as a first-order input voltage which includes the sum of a first-order input voltage signal and a variable voltage signal, and a variable gain amplifier which receives an amplified version of the differential between the non-inverted and inverted output signals from the third-order component generation circuit; a first-order component generation unit for receiving the input added voltage and for generating a first-order component; a constant generation unit for receiving a constant voltage signal and for generating a constant component; and an addition circuit for adding output signals from the third-order component generation unit, the first-order generation unit, and the constant generation unit.

The invention of the claim 2 is constructed so as to comprise the third-order component generator, the first-order component generation unit and the constant generation unit which have the respective compositions described in claim 1 and their outputs are added. Thus, the third-order function of the expression (2) can be generated accurately and the respective variables can be controlled independently.

An approximate third-order function generator of claim 3 is characterized in that in the invention of claim 1 or 2, the fourth amplifier has an output characteristics reverse in inclination to the inverted output characteristics of the second amplifier, and the distance between the maximum and minimum values of the output signal is set so as to be longer than that of the second amplifier.

In the invention of claim 3, an approximate first-order straight line can be generated in a range of input voltages which can be approximated by a third-order function which has been generated by the first-third amplifiers to thereby ensure that the first-order component contained in the third-order component is offset.

An approximate third-order function generator of claim 4 is characterized in that the first-fourth amplifiers each comprise a differential amplifier having a pair of MOS field effect transistors.

In the invention of claim 4, the approximate third-order function generator includes CMOSs to thereby achieve higher density integration and reduced power consumption.

A temperature compensated crystal oscillation circuit of claim 5 is characterized by a temperature detection circuit, a temperature compensation circuit which includes an approximate third-order function generator according to any one of claims 1-4 for receiving a detection signal from the temperature detection circuit, and a voltage-controlled crystal oscillation circuit for receiving the approximate third-order function generated by the temperature compensation circuit.

In the invention of claim 5, an accurate third-order function which is free from first-order component contained in the third-order component is generated, as described above, in the approximate third-order function generator of the temperature compensation circuit. The temperature characteristics of the crystal oscillator in the voltage-controlled crystal oscillation circuit is compensated accurately.

A temperature compensation adjusting method for a temperature compensated crystal oscillation circuit of claim 6 comprises the steps of measuring an output voltage V_(Cout) from a temperature compensation circuit in a predetermined temperature atmosphere; measuring an input voltage V_(Cin) to the voltage-controlled crystal oscillation circuit where the oscillation frequency output from the voltage-controlled crystal oscillation circuit coincides with a preset selected frequency at a respective one of a plurality of temperatures T in a desired temperature compensation range; approximately representing the measured input voltage V_(Cin) and output voltage V_(Cout) at the respective temperature by:

V _(Cin)(T)=α₃(T−T ₀)³+α₁(T−T ₀)+α₀

V _(Cout)(T)=β₃(T−T ₀′)³+β₁(T−T ₀′)+β₀;

and adjusting coefficients β₀, β₁, β₃ and T₀′ of the temperature compensation circuit so as to coincide with the coefficients α₀, α₁, α₃ and T₀, respectively, inherent to a crystal resonator of the voltage-controlled crystal oscillation circuit.

In the invention of claim 6, the output voltage V_(Cout) from the temperature compensation circuit and the input voltage V_(Cin) to the voltage-controlled crystal oscillation circuit are measured at the respective one of the plurality of temperatures in the desired temperature compensation range, and approximated by the corresponding third-order function expressions each as a function of a temperature. The coefficients of the temperature compensation circuit are adjusted so as to coincide with coefficients dependent on the crystal resonator of the voltage-controlled oscillation circuit and hence the temperature compensation is achieved by a single temperature sweeping operation.

As described above, according to the invention of claim 1, the approximate third-order function generator comprises a first amplifier, a second amplifier and a third amplifier, each receiving a common input signal and a different fixed level signal, the three different fixed level signals received by the first, second and third amplifiers sequentially increasing in level in this order, each amplifier having an input-output characteristics in which a non-inverted or inverted output signal is provided based on the common input signal and the fixed level signal concerned, that amplifier also having a function to limit the output signal to within a range defined by a maximum predetermined value and a minimum predetermined value; a fourth amplifier receiving the common input signal and the same fixed level signal as the second amplifier receives, the fourth amplifier having an input-output characteristics in which a non-inverted or inverted output signal is provided based on the common input signal and the fixed level signal concerned, and having a function to limit the output signal to within a range defined by an maximum predetermined value and a minimum predetermined value; and a fixed level signal generation circuit for supplying the fixed level signals having the different fixed levels to the first-fourth amplifiers, respectively, the output characteristics of the first, third and fourth amplifiers being set so as to have the same polarity, the output characteristics of the second amplifier being set so as to be reverse to those of the first, third and fourth amplifiers, the output signals from the first, second, third and fourth amplifiers being added to generate a third-order function component free from a first-order component. Thus, only the third-order component free from the first-order component in the third-order function is output. Thus, the variables of the third-order function can be controlled independently.

According to the invention of claim 2, the approximate third-order function generator comprises a third-order component generation unit which includes a third-order component generation circuit having the composition of claim 1 supplied with an input added voltage as a first-order input voltage which includes the sum of a first-order input voltage signal and a variable voltage signal, and a variable gain amplifier which receives an amplified version of the differential between the non-inverted and inverted output signals from the third-order component generation circuit; a first-order component generation unit for receiving the input added voltage and for generating a first-order component; a constant generation unit for receiving a constant voltage signal and for generating a constant component; and an addition circuit for adding output signals from the third-order component generation unit, the first-order generation unit, and the constant generation unit. Thus, by controlling independently the respective variables of a third-order component, a first-order component and a constant component obtained when a general-form third-order function is converted with respect to its variables, any third-order function is realized as a voltage input and a voltage output.

According to the invention of claim 3, the fourth amplifier has an output characteristics reverse in inclination to the inverted output characteristics of the second amplifier, and the distance between the maximum and minimum values of the output signal is set so as to be longer than that of the second amplifier. Thus, an approximate first-order straight line can be generated in a range of input voltages which can be approximated by a third-order function which has been generated by the first-third amplifiers to thereby ensure that the first-order component contained in the third-order component is offset.

According to the invention of claim 4, the first-fourth amplifiers each comprise a differential amplifier having a pair of MOS field effect transistors. Thus, the whole approximate third-order function generator has a CMOS composition to thereby achieve higher density integration and reduced power consumption.

According to the invention of claim 5, the temperature compensated crystal oscillation circuit comprises a temperature detection circuit, a temperature compensation circuit which includes an approximate third-order function generator according to any one of claims 1-4 for receiving a detection signal from the temperature detection circuit, and a voltage-controlled crystal oscillation circuit for receiving the approximate third-order function generated by the temperature compensation circuit. Thus, an accurate third-order function which is free from first-order component contained in the third-order component is generated, as described above, in the approximate third-order function generator of the temperature compensation circuit. Thus, the temperature characteristics of the crystal oscillator in the voltage-controlled crystal oscillation circuit is compensated accurately.

According to the invention of claim 6, the output voltage V_(Cout) from the temperature compensation circuit and the input voltage V_(Cin) to the voltage-controlled crystal oscillation circuit are measured at the respective one of the plurality of temperatures in the desired temperature compensation range, and approximated by the corresponding third-order function expressions each as a function of a temperature. The coefficients of the temperature compensation circuit are then adjusted so as to coincide with coefficients dependent on the crystal resonator of the voltage-controlled crystal circuit and hence a high-accuracy temperature compensation is achieved by a single temperature sweeping operation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an embodiment of the present invention;

FIG. 2 is a circuit diagram of a third-order component and constant component generation unit of FIG. 1;

FIG. 3 is a circuit diagram of one example of the third-order component generation circuit of FIG. 2;

FIG. 4 is a circuit diagram of one example of a constant voltage generation circuit of FIG. 1;

FIG. 5 is a diagram of an output waveform from a temperature detection circuit of FIG. 1;

FIG. 6 is a circuit diagram of one example of a first-order component generation unit of FIG. 1;

FIG. 7 is a basic circuit diagram used for explaining operation of the third-order generation circuit of FIG. 3;

FIG. 8 is an output waveform diagram of FIG. 7;

FIG. 9 is a circuit diagram of a basic third-order component generation unit of the third-order component generation circuit of FIG. 3;

FIG. 10 is a characteristics curve diagram of inverted output characteristics of the respective differential amplifiers used for explaining operation of the third-order component generation circuit of FIG. 3;

FIG. 11 is an output waveform diagram used for explaining operation of the third-order component generation circuit of FIG. 3;

FIG. 12 is a waveform diagram of an input-output characteristics of a fourth differential amplifier of FIG. 3;

FIG. 13 is an output waveform diagram used for explaining operation of the third-order function generator of FIG. 1;

FIG. 14 is a temperature characteristics diagram of a crystal resonator; and

FIG. 15 is an output waveform diagram of a prior-art third-order function generator.

Description of the Reference Numerals: 1 . . . Temperature Detection Circuit; 2 . . . Approximate Third-Order Function Generator; 100 . . . Voltage-Controlled Crystal Oscillator; 3 . . . Adder; 4 . . . Third-Order Component and Constant Component Generation Unit; 5 . . . First-Order Component Generation Unit; 7 . . . Adder Circuit; 8 . . . Third-Order Component Generation Circuit; 11 . . . Differential Amplifier; 12 . . . Variable Gain Amplifier; 14 . . . Current Mirror Circuit; 15A-15D . . . Differential Amplifiers; TrA₁-TrD₂ . . . MOS Field Effect Transistors; 16A, 16B . . . Output Voltage Adding Resistors; 17 . . . Fixed Level Generation Circuit; 18 . . . Constant Voltage Generation Circuit; VR . . . Variable Resistor; 20 . . . Non-inverting Amplifier.

BEST MODE FOR CARRYING OUT THE INVENTION

An embodiment of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram of an embodiment of a temperature compensated crystal oscillator to which the present invention is applied.

In FIG. 1, reference numeral 1 denotes a temperature detection circuit whose analog output voltage changes linearly depending on its temperature change. A detected temperature value of an analog voltage outputted from the temperature detection circuit 1 is inputted as an input signal V_(IN) to an approximate third-order function generator 2 to generate a control voltage to compensate the temperature characteristics of the crystal. The control voltage is then fed to a voltage-controlled crystal oscillator (VCXO) 100.

The temperature detection circuit 1 and the approximate third-order function generator 2 constitute a temperature compensation circuit. The approximate third-order function generator 2 generates the third-order function represented by the expression (2) and is comprised of an adder 3 which sums up the input signal V_(IN) and variable voltage V₀′, a third-order component and constant component generation unit 4 which receives a summed-up output V_(S) from the adder 3 and which generates a third-order component and constant component of the first term of the expression (2) based on the summed-up output V_(S), a first-order component generation unit 5 which generates a first-order component of a second term of the expression (2), and an addition circuit 7 which sums up output signals from the third-order component generation unit 4 and the first-order component generation unit 5.

As shown in FIG. 2, the third-order component and constant component generation unit 4 is comprised of a third-order component generation circuit 8 as an approximate third-order function generator in the narrow sense which generates only a third-order component, a differential amplifier 11 which receives a non-inverted output signal P_(OUT) and an inverted output signal N_(OUT) via buffer circuits 9 and 10, respectively, and a variable gain amplifier 12 which receives an output from the differential amplifier 11.

As shown in FIG. 3, the third-order component generation circuit 8 is comprised of a current mirror circuit 14 which includes a p-channel MOS field effect transistor Tr0 having a source connected to a positive power supply terminal V_(DD), and a gate and a drain connected together and grounded via a constant current source 13, and four p-channel MOS field effect transistors Tr1-Tr4 having gates connected to the gate of the field effect transistor Tr0 and having the same size as the transistor Tr0; four differential amplifiers 15A-15D which constitute first-fourth amplifiers each supplied with a constant current from the current mirror circuit 14; resistors 16A and 16B having the same resistance value and each functioning as an adder which sums up output voltages from the differential amplifiers 15A-15D; and a fixed level generation circuit 17 composed of a fixed voltage generation circuit which supplies reference fixed voltages V_(REFL), V_(REFM) and V_(REFH) different in level to the corresponding differential amplifiers 15A-15D.

The differential amplifier 15A includes p-channel MOS field effect transistors TrA₁ and TrA₂ connected in series via resistors RA₁ and RA₂ to the drain of the field effect transistor Tr1 of the current mirror circuit 14. An input signal V_(IN) is supplied to the gate of the transistor TrA, and the reference fixed voltage V_(REFL) is supplied from the fixed level generation circuit 17 to the gate of the transistor TrA₂. The drain of the transistor TrA₁ is grounded via the resistor 16A which constitutes the adder whereas the drain of the transistor TrA₂ is grounded via the other resistor 16B which constitutes the other adder.

Similarly, the differential amplifier 15B includes p-channel MOS field effect transistors TrB₁ and TrB₂ connected in series via resistors RB₁ and RB₂ to the drain of the field effect transistor Tr2 of the current mirror circuit 14. An input signal V_(In) is supplied to the gate of the transistor TrB₁ and the reference fixed voltage V_(REFM) is supplied from the fixed level generation circuit 17 to the gate of the transistor TrB₂. Unlike the case of the differential amplifier 15A, the drain of the transistor TrB₁ is grounded via the resistor 16B which constitutes the adder whereas the drain of the transistor TrB₂ is grounded via the other resistor 16A which constitutes the other adder. The inverted output characteristics of the differential amplifier 15B is set, for example, reverse to the differential amplifiers 15A, 15C and 15D.

Like the differential amplifier 15A, the differential amplifier 15C includes p-channel MOS field effect transistors TrC₁ and TrC₂ connected in series via resistors RC₁ and RC₂ to the drain of the field effect transistor Tr3 of the current mirror circuit 14. An input signal V_(In) is supplied to the gate of the transistor TrC₁ and the reference fixed voltage V_(REFH) is supplied from the fixed level generation circuit 17 to the gate of the transistor TrC₂. The drain of the transistor TrC₁ is grounded via the resistor 16A which constitute the adder whereas the drain of the transistor TrC₂ is grounded via the other resistor 16B which constitute the other adder.

Like the differential amplifiers 15A and 15C, the differential amplifier 15D includes p-channel MOS field effect transistors TrD₁ and TrD₂ connected in series via resistors RD₁ and RD₂ to the drain of the field effect transistor Tr4 of the current mirror circuit 14. An input signal V_(In) is supplied to the gate of the transistor TrD₁ and the reference fixed voltage V_(REFM) is supplied from the fixed level generation circuit 17 to the gate of the transistor TrD₂. Unlike the case of the differential amplifiers 15A-15C, the drain of the transistor TrD₁ is grounded via the resistor 16B which constitutes the adder whereas the drain of the transistor TrD₂ is grounded via the other resistor 16A which constitutes the other adder.

A non-inverted output terminal to is connected to the junction of the resistor 16A which constitutes the adder, and the field effect transistors TrA₁, TrB₂, TrC₁ and TrD₁. Similarly, an inverted output terminal t_(N) is connected to the junction of the resistor 16, and the field effect transistors TrA₂, TrB₁, TrC₂ and TrD₂.

The respective levels of the reference fixed voltages V_(REFH)-V_(REFL) generated by the fixed level generation circuit 17 and supplied to the respective differential amplifiers 15A-15C are set by V_(REFL)<V_(REFM) <V_(REFH) so that the differential amplifier 15D is also supplied with the same reference fixed voltage V_(REFM) as that supplied to the differential amplifier 15B.

As shown in FIG. 2, the non-inverted and inverted output signals P_(OUT) and N_(OUT) from the third-order component generation circuit 8 are supplied via the buffer circuits 9 and 10 to the non-inverted and inverted inputs, respectively, of a differential amplifier 1. An output signal from the differential amplifier 11 is supplied to an inverting input of an operational amplifier 12 b via a variable resistor 12 a intervening in a negative feedback circuit which constitutes a part of a variable gain amplifier 12. Any set offset voltage V_(OFF) is supplied from a constant voltage generation circuit 18 to normal inputs to the operational amplifier 12 b and the differential amplifier 11. Thus, the operational amplifier 12 b provides an output VA_(OUT) which contains only a third-order component free from a first-order component and a constant component, represented by:

VA _(OUT) =b ₃(V _(In) −V ₀)³ +V _(OFF)  (5)

where V₀=V_(REFM)−V₀′, and the variable b₃ is determined by the gains of the third-order component generation circuit 8 and the variable gain amplifier 12.

As shown in FIG. 4, the constant voltage generation circuit 18 is comprised of an operational amplifier 30, a bipolar transistor Q₁ whose collector and base are connected together via a resistor 31 to the output of the operational amplifier 30 and whose emitter is connected to a negative output terminal t_(N) of the operational amplifier 30 to form a diode connection, and a bipolar transistor Q₂ whose collector and base are connected together via resistors 32 and 33 to the output of the operational amplifier 30. A junction point of the resistors 32 and 33 is connected to the inverting input of the operational amplifier 30. A junction point of the resistor 31 and transistor Q₁ is connected to the non-inverting input of the operational amplifier 30 with a positive output terminal to being connected to the output of the operational amplifier 30 to thereby constitute a band gap reference voltage circuit.

In this band gap reference voltage circuit, a voltage differential ΔV_(BE) between the base-emitter voltages of the transistors Q₂ and Q₁ applied across the resistor 33 is represented by:

ΔV _(BE) =V _(T) ln{(I ₁ /I ₂)(I _(S2) /I _(S1))}=V _(T) ln{(R ₁ /R ₂)(I _(S2) /I _(S1))}  (6)

where V_(T) is a thermal voltage, I₁ is the value of a current flowing through the resistor 31, I₂ is the value of a current flowing through the resistor 32, I_(S1) is a constant which represents a transmission characteristics of a forward active area of the transistor Q₁, I_(S2) is a constant which represents a transmission characteristics of a forward active area of the transistor Q₂, R₁ is the resistance value of the resistor 31, and R₂ is the resistance value of the resistor 32.

Since the same current as flows through the resistor 33 flows through the resistor 32, a voltage drop V_(R2) across the resistor 32 is represented by:

V _(R2)=(R ₂ /R ₃)ΔV _(BE)=(R ₂ /R ₃)V _(T) ln{(R ₂ /R ₁)(I _(S2) /I _(S1))}  (7)

As is obvious form the expression, (7), if the temperature coefficients of the resistors are zero, the currents I₁ and I₂ are together proportional to temperature, so that the output voltage V_(OUT) across the output terminals t_(P) and t_(N) is represented by:

 V _(OUT) =V _(BE1)+(R ₂ /R ₃)V _(T) ln{(R ₂ /R ₁)(I _(S2) /I _(S1))}=V _(BE1) +KV _(T)  (8)

where V_(BE1) is the base-emitter voltage of the transistor Q₁, and K is a constant.

Thus, since the base-emitter voltage V_(BE1) of the transistor Q₁ having a temperature dependent property and KV_(T) having an inverted characteristics are added, the value of the constant K is determined by the ratios (R₂/R₁), (R₂/R₃) and (I_(S2)/I_(S1)) to produce a constant voltage irrespective of a change in the temperature.

Since the difference ΔV_(BE) between the base-emitter voltages V_(BE) of the transistors Q₂ and Q₁ of the set forth band gap reference voltage circuit changes linearly depending on temperature, the temperature detection circuit 1 uses the base-emitter voltage difference ΔV_(BE). Thus, a sensed temperature value is output which comprises an analog voltage value increasing linearly depending on temperature, as shown in FIG. 5, without using a thermistor whose resistance changes linearly depending on temperature.

As shown in FIG. 6, the first-order component generation unit 5 is comprised of a variable resistor VR connected across the adder 3 and a reference fixed voltage input terminal t_(R), a non-inverting amplifier 20 having a non-inverting input connected to a slider of the variable resistor VR and having an inverting input connected to the reference fixed voltage input terminal t_(R) via a resistor R₁, with the output signal from the amplifier 20 being fed back to its inverting input and with the referent fixed voltage input terminal t_(R) being supplied with the reference fixed voltage V_(REFM) from the third-order component generation circuit 8.

According to the first-order component generating unit 5, the non-inverting amplifier 20 amplifies the difference between the input signal V_(In) and the differential between the reference fixed voltage V_(REFM) and the variable voltage V₀′ to provide an output voltage VB_(OUT) represented by:

VB _(OUT) =b ₁(V _(In) −V ₀)+V _(REFM)  (9)

where V₀=V_(REFM)−V₀′, and the variable b₁ is determined by a set value of the variable resistor VR and the gain of the non-inverting amplifier 20.

Operation of the embodiment will be described next.

First, operation of the approximate third-order function generator 2 will be described.

In order to simplify the explanation of the operation of the third-order component generation circuit 8, one differential amplifier 15A will be described as an example, as shown in FIG.7. When the input voltage V_(In) is sufficiently low compared to the reference voltage V_(REFL), the whole current which flows through the transistor Tr 1 also flows through the transistor TrA₁. Let a constant current value of the current mirror circuit 14 be I₀. In this case, a current I_(A1) which flows through the transistor TrA₁ becomes I₀ and a current I_(A2) which flows through the transistor TrA₂ becomes zero. Thus, the output voltages P_(OUT) and N_(OUT) at the output terminals t_(P) and t_(N) are I₀R_(R) and zero, as shown in broken and solid lines, respectively, in FIG. 8 where R_(B) is the resistance value of each of the resistors 16A and 16B.

When the input voltage V_(In) increases from this state and exceeds a value V_(AL) which represents the reference fixed voltage V_(REFL) minus a voltage drop I₀·R_(A) across the resister RA₁, the output voltage P_(OUT) gradually decreases smoothly. In contrast, when the output voltage N_(OUT) gradually increases smoothly and the input voltage V_(IN) equals the reference fixed voltage V_(REFL), the output voltage P_(OUT) equals the output voltage N_(OUT). When the input voltage V_(IN) further increases, the output voltage P_(OUT) maintains its decreasing tendency, and the output voltage N_(OUT) maintains its increasing tendency. When the input voltage V_(IN) exceeds a value V_(AH) which includes the sum of the reference fixed voltage V_(REFL) and the voltage drop I₀·R_(A) across the resistor RA₂, the output voltage P_(OUT) becomes zero whereas, conversely, the output voltage N_(OUT) becomes I₀·R_(B).

Eventually, in the output characteristics of FIG. 8, it is smooth output changes in the vicinity of V_(REFL)±I₀R_(A) that is determined only by the resistance values R_(A) of the resistors RA₁ and RA₂ and the constant current value I₀ of the current mirror circuit 10, depending on the characteristics of the transistors.

Now, a circuit of FIG. 9 which is obtained by eliminating the fourth differential amplifier 15D from the third-order component generation circuit 8 of FIG. 3 is considered. When the input voltage V_(IN) is sufficiently low compared to the reference fixed voltage V_(REFL) (V_(IN)<<V_(REFH)), the whole current which flows through the transistor Tr1 in the differential amplifier 15A flows through the transistor TrA₁, as mentioned above. As a result, I_(A1)=I₀, and I_(A2)=0. Similarly, also in the differential amplifiers 15B and 15C, I_(B1)=I_(C1)=I₀, and I_(B2)=I_(C2)=0. The currents I_(P) and I_(N) which flow through the resistors 16A and 16B which constitute the respective adders become I_(P)=2I₀ and I_(P)=I₀.

When the input voltage V_(IN) increases, a current starts to flow through the transistor TrA₂ whereas the current which flows through the transistor TrA₁ starts to decrease until the input voltage V_(IN) reaches the reference fixed voltage V_(REFL), at which time I_(A1)=I_(A2)=I₀/2. No other differential amplifiers 15B and 15C change their states, so that the output currents I_(N) and I_(P) become I_(N)=I_(P)=3I₀/2. When the input voltage V_(IN) further increases, I_(A1)=0, and I_(A2)=I₀. Thus, the output currents I_(P) and I_(N) become I_(P)=I₀, and I_(N)=2I₀.

When the input voltage V_(IN) further increases, a current starts to flow through the transistor TrB₂ of the differential amplifier 15B, and the current flowing through the transistor TrB₁ starts to decrease until the input voltage V_(IN) reaches the reference fixed voltage V_(REFM), at which time I_(B1)=I_(B2)=I₀2, and the output currents I_(P) and I_(N) again become I_(N)=I_(P)=3I₀/2.

When the input voltage V_(IN) further increases appropriately, I_(P)=I₀, and I_(N)=2I₀. Then, when the input voltage V_(IN) reaches the reference fixed voltage V_(REFH), the output voltage I_(P) and I_(N) again become I_(P)=I_(N)=3I₀2. Then, when the input voltage V_(IN) further increases appropriately, I_(P)=2I₀, and I_(N)=I₀.

Thus, for example, as for the inverting terminal t_(N) side, the output current I_(A2) of the first differential amplifier 15A, as shown by a dot-dashed line in FIG. 10, maintains zero until the input signal voltage V_(IN) reaches a minimum value V_(AL) in the first differential amplifier 15A. When the input signal voltage V_(IN) exceeds the minimum value V_(AL), the output current I_(A2) of the first differential amplifier 15A starts to increase until the input signal voltage reaches the reference fixed voltage V_(REFL), at which time,the output current becomes I₀/2. Also, thereafter, the output current increases depending on an increase in the voltage of the input signal V_(IN) until it reaches I₀ at a maximum value V_(AH) of the input signal voltage to become saturated.

The output current I_(B1) from the second differential amplifier 15B, as shown by broken lines in FIG. 10, maintains I₀ until the voltage of the input signal V_(IN) reaches the minimum value V_(BL) (in the present embodiment, set to a value equal to V_(AH)) in the second differential amplifier 15B. When the voltage of the input signal V_(IN) exceeds the minimum value V_(BL), the output current I_(A1) from the second differential amplifier 15B decreases as the voltage of the input signal V_(IN) increases until the voltage of the input signal V_(IN) reaches the reference fixed voltage V_(REFM), at which time the output current I_(A1) becomes I₀/2. Thereafter, as the voltage of the input signal V_(IN) increases, the output current I^(A1) decreases, and then maintains zero when the voltage of the input signal V_(IN) exceeds the maximum value V_(BH).

The output current I_(C2) from the third differential amplifier 15C, as shown by a dot-dashed line in FIG. 10, maintains zero until the voltage of the input signal voltage V_(IN) reaches a minimum value V_(CL) in the third differential amplifier 15C (which is set at a value equal to V_(BH) in the particular embodiment). When the input signal voltage V_(IN) exceeds the minimum value V_(CL), the output current I_(C2) from the first differential amplifier 15C starts to increase until the input signal voltage reaches the reference fixed voltage V_(REFH), at which time the output current becomes I₀/2. Also, thereafter, the output current increases depending on an increase in the voltage of the input signal V_(IN) until it reaches I₀ corresponding to a maxim value V_(CH) of the input signal voltage to become saturated.

Thus, the output voltages P_(OUT) and N_(OUT) at the output terminals t_(P) and t_(N) are represented as P_(OUT)=I_(P)·R_(B), and N_(OUT)·R_(B) and the currents I_(P) and I_(N) flowing through those resistors by the resistors 16A and 16B. By adjusting the circuit constants, a smooth third-order curve is obtained which is shown by a broken-line characteristics curve L₁ in FIG. 11.

The characteristics curve L₁ of FIG. 11 includes the sum of the third-order function and a linear function having a negative inclination, which does not represent only the third-order component of the first term of the expression (2).

Thus, in the present embodiment, the fourth differential amplifier 15D is additionally provided to generate a linear function having a positive inclination which offsets the. linear function having the negative inclination.

The fourth differential amplifier 15D has a composition similar to those of the first and third differential amplifiers 15A and 15C, so that in its input/output characteristics of FIG. 12, the inclination of an area approximate to the linear function is reduced by increasing the resistance values of the resistors RD₁ and RD₂ and that the distance between the minimum value V_(DL) and the maximum value V_(DH) and hence the area approximate to the linear function are increased. Also, by increasing the values of the currents fed to the resitors RD₁ and RD₂, the area approximate to the liner function can be increased.

Thus, by adjusting the resistance values R_(D) of the resistors RD₁ and RD₂ of the fourth differential amplifier 15D and the values of the currents fed to the resistors RD₁ and RD₂ to change the input-output characteristics of the amplifier 15D so that the minimum value V_(DL) and the maximum value V_(DR) coincide with the minimum value V_(AL) of the first differential amplifier 15A and the maximum value V_(CH) of the third differential amplifier 15C, respectively, as shown by a dot-dot dashed line in FIG. 10, an input/output characteristics is obtained which is represented by an approximate linear characteristics curve L₂ as shown by a dot-dash line in FIG. 11. By adding the characteristics curve L₂ to the characteristics curve L₁, only a third-order component is obtained which is free form the linear function component, as shown by a solid-line characteristics curve L₃ in FIG. 11.

By supplying the non-inverted output signal P_(OUT) and inverted output signal N_(OUT) of the third-order component generation circuit 8 via the buffer circuits 9 and 10, respectively, to the differential amplifier 11, which, in turn, supplies its output signal to the variable gain amplifier 12, and by supplying an offset voltage V_(OFF) from the constant voltage circuit 18 to the non-inverting inputs of the differential amplifier 11 and the variable gain amplifier 12, an output voltage VA_(OUT) which includes only the third-order component and constant component free from the first-order component, as represented by the expression (5), is obtained from the variable gain amplifier 12.

The first-order component generation unit 5 provides an output voltage VB_(OUT) which includes only the first-order component and constant component represented by the expression (6). Thus, by adding the output voltage VB_(OUT) to the output voltage VA_(OUT) of the third-order component generation unit 4 in the addition circuit 7, an approximate third-order function is generated which is represented by:

V _(OUT) =b ₃′(V _(IN) −V ₀)³ +b ₁′(V _(IN) −V ₀)+b ₀′  (10)

where V₀ can be set at any value by adjusting the variable voltage V₀′. The third-order component variable b₃′ is adjustable with copy by adjusting the gains of the third-order component generation circuit 8 and the variable gain amplifier 12, as described above. The first-order component variable b₁′ is adjustable by adjusting the resistance value of the variable resistor VR and the gain of the non-inverting amplifier 20 of the first-order component generation unit 5. A constant b₀′ is adjustable by an offset voltage V_(OFF) set in the constant voltage circuit 18. The respective variables are adjustable independently to generate any third-order function such as is shown in FIG. 13.

The current mirror circuit 10 and the differential amplifiers 15A-15D of the third-order component generation circuit 8 can be all composed of CMOS transistors to thereby achieve higher integration and lower power consumption.

By applying the present invention to the temperature compensated crystal oscillator as in the embodiment, the crystal resonator included in the voltage-controlled crystal oscillation circuit 3 has a general oscillation frequency-temperature characteristics such as shown in FIG. 14 where the horizontal axis represents temperature (° C.) and the vertical axis frequency (ppm). The temperature characteristics is approximated by:

Y=α×(t−t ₀)³+β×(t−t ₀)+γ  (11)

where Y is the output frequency, α is a third-order coefficient, β is a inclination of the temperature characteristics, γ is a frequency offset, t is a atmospheric temperature, and t₀ is a temperature at the center of the curve Y (usually, in an arrange of 25-30° C.).

The coefficients and constant α, β and γ in the expression (11) are dependent on the characteristics of the crystal resonator and the voltage-controlled crystal oscillation circuit 8, especially greatly on the crystal resonator, and more particularly, on its shape and size.

The voltage-frequency characteristics of the voltage-controlled crystal oscillation circuit 8 used widely at present can be approximated by a linear function, so that temperature-frequency characteristics of the crystal resonator is realized by its temperature-voltage characteristics.

Thus, in the embodiment of FIG. 1, voltages corresponding to the first, second and third terms of the right side of the expression (11) are generated by the approximate third-order curve generator 2 on the basis of a detected temperature signal from the temperature detection circuit 1; where there are possible deviations between solids in the third-order term coefficient α, temperature characteristics inclination β, and frequency offset γ of the generator 2 from their standard values, these are respectively adjusted finely by adjusting the gain of the third-order component generation circuit 8 and/or the gain of the variable gain amplifier 12 and the output voltage V_(OFF) of the constant voltage circuit 18 of the third-order component generation unit 4, and/or the resistance value of the variable resistor VR and/or the gain of the non-inverted amplifier 20 of the first-order component generation unit 5; the respective voltages obtained after the fine adjustments are added in the addition circuit 7 to obtain a control voltage for the voltage-controlled crystal oscillation circuit 8 corresponding to the temperature-frequency characteristics of the crystal resonator of FIG. 14; the control voltage is then supplied to the voltage-controlled crystal oscillation circuit 8 to accurately compensate the temperature dependant characteristics of the crystal resonator included in the oscillation circuit 8.

Specifically, the approximate third-order function generator 2 and the voltage-controlled crystal oscillator (VCXO)100 of FIG. 1 are separately placed within the respective constant temperature tanks, whose temperatures are set at any respective particular temperatures in a range of temperatures in which the temperature compensation is desired.

In a state where the tank temperatures are stabilized at their set temperatures, the input voltage V_(Cin) to the voltage-controlled crystal oscillator 100 is changed, so that the input voltage V_(Cin1) where the frequency of the output signal coincides with the preset frequency is measured, and the output voltages V_(Cout1) from the temperature compensation circuit comprised of the temperature detection circuit 1 and the third-order function generator 2 is measured.

The above measurements are repeated twice or more, preferably four times or more, by raising the set temperatures of said tanks sequentially to different higher temperatures, so that the input voltages V_(Cin1)−V_(CinN) to the voltage-controlled crystal oscillator 100 and the output voltage V_(CoutN) of the third-order function generator 2 are obtained at the respective set temperatures.

Then, the respective measured input voltages V_(Cin1)−V_(CinN) and output voltages V_(Cout1)−V_(CoutN) are approximated, respectively, as functions of temperature by:

V _(Cin)(T)=α₃(T−T ₀)³+α₁(T−T ₀)+α₀  (12)

V _(Cout)(T)=β₃(T−T ₀′)³+β₁(T−T ₀′)+β₀  (13)

where α₃, α₁ and α₀ of the expression (12) correspond to α,β and γ of the expression (11), and are dependent on the crystal resonator concerned.

By adjusting β₃, β₁, β₀ and T₀′ in the approximate third-order function generator 2 to be β₃=α₃, β₁=α₁,β₀=α₀ and T₀′=T₀, high-accuracy temperature compensation is achieved only by a single temperature sweeping operation.

The approximate third-order function generator 2 is specifically adjusted as follow: The central temperature T₀′ of the third-order function curve of the expression (13) is adjusted by a variable voltage V₀′ applied to the addition circuit 3 of FIG. 1. The constant β₀ is adjusted by an offset voltage V_(OFF) output from the constant voltage generation circuit 18 of FIG. 2. The first-order, term coefficient β₁ is adjusted by the variable resistor VR of the first-order component generation unit 5 of FIG. 6. The third-order term coefficient β₃ is adjusted by the variable resistor 12 a of the variable gain amplifier 12 of FIG. 2 in the third-order component and constant component generation unit 4.

Thus, by raising the tank temperatures sequentially to four or more different temperatures, the output voltage from the temperature compensation circuit, i.e. the output voltage V_(Cout) from the approximate third-order function generator 2 and the input voltage V_(Cin) to the voltage-controlled crystal oscillation circuit 100 are respectively measured at the respective temperatures, the approximate third-order function generator 2 is adjusted on the basis of-the results of those measurements. That is, high-accuracy temperature compensation is achieved by a single temperature sweeping operation.

According to the embodiment, the temperature detection circuit 1 and the approximate third-order function generator 2 are constructed by a band gap reference voltage circuit which has an analog circuit composition using bipolar transistors, and the approximate third-order curve generation circuit 2 is constructed by an analog circuit which includes the current mirror circuit 14, differential amplifiers 15A-15D and resistors 16A and 16B, and hence all the components excluding the crystal resonator are integrated.

While in the embodiment the third-order component generation unit 4 has been illustrated as using p-channel MOS field effect transistors, the present invention is not limited to this particular case. For example, the third-order component generation circuit 8 may include n-channel MOS field effect transistors or otherwise bipolar transistors instead of the field effect transistors to produce beneficial effects similar to those mentioned above.

While in the embodiment the third-order component and constant component generation circuit 4 has been illustrated as generating the third-order components and constant components, the present invention is not limited to this particular case. For example, arrangement may be such that by removing the constant voltage generation circuit 18 from the third-order component and constant component generation unit 4, only the third-order component is output; the output from the constant voltage generation circuit 18 is supplied to a constant-component generation unit having a structure similar to that of the first-order component generation unit 5 of FIG. 6; the output voltage from the constant component generation unit, the output signal from the third-order component generation circuit and the output signal from the first-order component generation unit 5 are added in the addition circuit 7; and the resulting signal is then supplied to the voltage-controlled crystal oscillator 8.

While in the embodiment the voltage-controlled crystal oscillation circuit 8 has been described which includes the crystal resonator and the C-MOS inverter connected in series, the present invention is not limited to this particular case. For example, the crystal resonator and the C-MOS inverter may be connected in parallel to constitute a voltage-controlled crystal oscillation circuit. Alternatively, a voltage-controlled crystal oscillation circuit which includes transistors instead of the C-MOS inverter may be used.

The circuit composition of the third-order component generation circuit 8 and others in the embodiment may employ a current reference system instead of the voltage reference, and further employ a ground reference system using n-channel MOSFETs instead of the V_(DD) reference using the p-channel MOSFETs. 

What is claimed is:
 1. An approximate third-order function generator, comprising: a first amplifier, a second amplifier and a third amplifier, each receiving a common input signal and a different fixed level signal, the three different fixed level signals received respectively by the first, second and third amplifiers sequentially increasing in level in this order, each amplifier having an input-output characteristics in which a non-inverted or inverted output signal is provided based on the common input signal and the fixed level signal concerned, that amplifier also having a function to limit the output signal to within a range defined by a maximum predetermined value and a minimum predetermined value; a fourth amplifier receiving the common input signal and the same fixed level signal as said second amplifier receives, said fourth amplifier having input-output characteristics in which a non-inverted or inverted output signal is provided based on the common input signal and the fixed level signal concerned, and having a function to limit the output signal to within a range defined by an maximum predetermined value and a minimum predetermined value; and a fixed level signal generation circuit for supplying the fixed level signals having the different fixed levels to said first, second, third, and fourth amplifiers, respectively, the output characteristics of said first, third and fourth amplifiers being set so as to have a same polarity, the output characteristics of the second amplifier being set so as to be inverted to those of said first, third, and fourth amplifiers, wherein the output signals from said first, second, third and fourth amplifiers being added to generate a third-order function component free from a first-order component.
 2. An approximate third-order function generator, comprising: a third-order component generation unit which includes a third-order component generation circuit of claim 1 supplied with an input added voltage as a first-order input voltage which includes the sum of a first-order input voltage signal and a variable voltage signal, and a variable gain amplifier which receives an amplified version of a differential between the non-inverted and inverted output signals from said third-order component generation circuit; a first-order component generation unit for receiving the input added input voltage and for generating a first-order component; a constant generation unit for receiving a constant voltage signal and for generating a constant component; and an addition circuit for adding output signals from said third-order component generation unit, said first-order generation unit, and said constant generation unit.
 3. An approximate third-order function generator according to claim 1 or 2, wherein said fourth amplifier has an output characteristics reverse in inclination to the reverse output characteristics of said second amplifier, and the distance between the maximum and minimum values of the output signal is set so as to be longer than that of said second amplifier.
 4. An approximate third-order function generator according to claim 1, wherein the first, second, third, and fourth amplifiers each comprises a differential amplifier having a pair of MOS field effects transistors.
 5. A temperature compensated crystal oscillation circuit, comprising: a temperature detection circuit, an approximate third-order function generator for receiving a detection signal from said temperature detection circuit, and a voltage-controlled crystal oscillation circuit for receiving an approximate third-order function generated by said approximate third-order function generator; wherein said approximate third-order function generator comprises a first amplifier, a second amplifier and a third amplifier, each for receiving a common input signal and a different fixed level signal, the three different fixed level signals received respectively by the first, second and third amplifiers sequentially increasing in level in such order, each amplifier having input-output characteristics in which a non-inverted or inverted output signal is provided and based on the common input signal and the respective fixed level signal such amplifier also having a function to limit the output signal to within a range defined by a maximum predetermined value and a minimum predetermined value; a fourth amplifier for receiving the common input signal and the same fixed level signal as said second amplifier receives, said fourth amplifier having input-output characteristics in which a non-inverted or inverted output signal is provided based on the common input signal and the respective fixed level signal, and having a function to limit the output signal to within a range defined by a maximum predetermined value and a minimum predetermined value; and a fixed level signal generation circuit for supplying the fixed level signals having the different fixed levels to said first, second, third, and fourth amplifiers, respectively, the output characteristics of said first, third, and fourth amplifiers being set so as to have a same polarity, the output characteristics of the second amplifier being set so as to be inverted to those of said first, third and fourth amplifiers, wherein the output signals from said first, second, third, and fourth amplifiers being added to generate a third-order function component free from a first-order component.
 6. A temperature compensation adjusting method for a temperature compensated crystal oscillation circuit, comprising the steps of: measuring an output voltage V_(Count) from a temperature compensation circuit in a predetermined temperature atmosphere; measuring an input voltage V_(Cin) to said a voltage-controlled crystal oscillation circuit where an oscillation frequency output from said voltage-controlled crystal oscillation circuit coincides with a preset selected frequency at a respective one of a plurality of temperatures T in a desired temperature compensation range; approximately representing the measured input voltage V_(Cin) and output voltage V_(Cout) at a respective temperature by: V _(Cin)(T)=α₃(T−T ₀)³+α₁(T−T ₀)+α₀ V _(Cout)(T)=β₃(T−T ₀′)³+β₁(T−T ₀′)+β₀; adjusting coefficients β₀, β₁, β3 and T₀′ of the temperature compensation circuit so as to coincide with the coefficients α₀, α₁, α₃, and T₀, respectively, inherent to a crystal resonator of the voltage-controlled crystal oscillation circuit.
 7. An approximate third-order function generator, comprising: a third-order component generation unit in which a third-order component generation circuit as set forth in claim 5 is supplied with an input added voltage as a first-order input voltage which includes the sum of a first-order input voltage signal and a variable voltage signal, and a variable gain amplifier which receives an amplified version of the differential between the non-inverted and inverted output signals from said third-order component generation circuit; first-order component generation unit for receiving the input added input voltage and for generating a first-order component; a constant generation unit for receiving a constant voltage signal and for generating a constant component; and an addition circuit for adding output signals from said third-order component generation unit, said first-order generation unit, and said constant generation unit.
 8. An approximate third-order function generator according to claim 5 or 7, wherein said fourth amplifier has output characteristics reverse in inclination to the reverse output characteristics of said second amplifier, and the distance between the maximum and minimum values of the output signal is set so as to be longer than that of said second amplifier. 